Physics

• A scalar is a quantity with magnitude ONLY
• Examples of scalars: time, distance, speed, mass, energy
• A vector is a quantity with magnitude AND direction
• Examples of vectors: velocity, acceleration, weight, force
• A resultant vector is a single vector which has the same effect as two or more vectors added together
• A bearing is an angle measured clockwise from north
• Vectors are represented using arrows
• Magnitude of Vector (Length of Arrow)
• Direction of Vector = Direction of Arrow
• If individual vectors are in 1 dimension, the resultant vector can be found using vector addition
• If individual vectors are in 2 dimensions, the resultant vector can be found using:

  • Tail-to-Head Method (by construction)
  • Component Method (using mathematics)
• Arrange vectors tail-to-head, with the tail of one vector touching the head of the other
• The resultant vector is the vector drawn from the tail of the first vector to the head of the last vector
• Vectors can be moved without changing their magnitude or direction
• The order in which you arrange the vectors is arbitrary (it does not matter)
• A vector diagram shows all the forces acting on an object drawn tail-to-head
• In an open vector diagram, there is a (non-zero) resultant vector
• In a closed vector diagram, there is no resultant vector
• Two forces are in equilibrium if they are equal in magnitude but opposite in direction
• Three (or more) forces are in equilibrium if they form a closed vector diagram, meaning there is no resultant force
• Three (or more) forces are NOT in equilibrium if they form an open vector diagram, meaning there IS a resultant force
• If forces are in equilibrium, then there is no resultant force
• The equilibrant force is the force that brings equilibrium, equal in magnitude but opposite in direction to the resultant force
• Forces acting on a stationary or object moving at a constant velocity are in equilibrium
• Every vector in two dimensions can be split into a horizontal and vertical component
• The horizontal component is also referred to as the horizontal component, and the vertical component as the vertical component
• Resolve each vector into its horizontal and vertical components using trigonometry
• Add the horizontal components together to get the resultant parallel to the x-axis, and the vertical components together to get the resultant parallel to the y-axis
• Use Pythagoras’ Theorem to compute the magnitude of the resultant vector: R^2 = Rx^2 + Ry^2
• Use trigonometry to compute the direction of the resultant vector (used to find a resultant vector in 2D)
• A force is a push or pull
• A force is a vector quantity, meaning it has both magnitude and direction
• A force is measured in Newtons (N)
• 1 N = 1 kg.m.s^-2
• Types of forces:

  • Contact force: in direct contact with the object it acts on
  • Field force: not in direct contact with the object, acts over a distance
• Force Definitions:

  1. Weight (Fg or W) - force with which an object is attracted to the Earth

  2. Normal force (FN or N) - force exerted by a surface on an object in contact, perpendicular to the surface

  3. Friction (Ff or f) - force that opposes motion of an object, acts parallel to the surface

  4. Tension (FT or T) - pulling force transmitted by a rope, string, cable, or chain

  5. Applied force (FA) - any force applied to an object by another object or person
• Weight (Fg or W):

  • Earth exerts force of gravity (Fg) on all objects within its gravitational field
  • Fg always acts vertically downwards, pulling objects towards Earth's centre
  • Fg = mg, where m = mass of the object (in kg) and g = 9.8 m.s^-2 down
• Normal force (FN or N):

  • Always acts perpendicular to the surface, regardless of surface orientation
• Friction (Ff or f):

  • Always acts parallel to the surface, regardless of surface orientation
  • Two types: Static frictional force (fs) and Kinetic frictional force (fk)
  • Motion is not necessary for friction to be present
• Tension (FT or T):

  • Force of tension has the same magnitude within the same piece of rope, string, cable, or chain if inextensible
  • If tension magnitude varies, there is a non-zero net force causing stretching, compression, or snapping